Necessary Optimality Conditions for a Lotka-Volterra Three Species System

N. C. Apreutesei

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 1, Issue: 1, page 120-132
  • ISSN: 0973-5348

Abstract

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An optimal control problem is studied for a Lotka-Volterra system of three differential equations. It models an ecosystem of three species which coexist. The species are supposed to be separated from each others. Mathematically, this is modeled with the aid of two control variables. Some necessary conditions of optimality are found in order to maximize the total number of individuals at the end of a given time interval.

How to cite

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Apreutesei, N. C.. "Necessary Optimality Conditions for a Lotka-Volterra Three Species System." Mathematical Modelling of Natural Phenomena 1.1 (2010): 120-132. <http://eudml.org/doc/222366>.

@article{Apreutesei2010,
abstract = { An optimal control problem is studied for a Lotka-Volterra system of three differential equations. It models an ecosystem of three species which coexist. The species are supposed to be separated from each others. Mathematically, this is modeled with the aid of two control variables. Some necessary conditions of optimality are found in order to maximize the total number of individuals at the end of a given time interval. },
author = {Apreutesei, N. C.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {adjoint system; bang-bang control; cost functional; Pontrjagin's maximum principle; transversality conditions},
language = {eng},
month = {3},
number = {1},
pages = {120-132},
publisher = {EDP Sciences},
title = {Necessary Optimality Conditions for a Lotka-Volterra Three Species System},
url = {http://eudml.org/doc/222366},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Apreutesei, N. C.
TI - Necessary Optimality Conditions for a Lotka-Volterra Three Species System
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 1
IS - 1
SP - 120
EP - 132
AB - An optimal control problem is studied for a Lotka-Volterra system of three differential equations. It models an ecosystem of three species which coexist. The species are supposed to be separated from each others. Mathematically, this is modeled with the aid of two control variables. Some necessary conditions of optimality are found in order to maximize the total number of individuals at the end of a given time interval.
LA - eng
KW - adjoint system; bang-bang control; cost functional; Pontrjagin's maximum principle; transversality conditions
UR - http://eudml.org/doc/222366
ER -

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